The book is an authoritative and up-to-date introduction to the field of Analysis and Potential Theory dealing with the distribution zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compact sets and on the real line. The main feature of the book is the combination of potential theory with conformal invariants, such as module of a family of curves and harmonic measure, to derive discrepancy estimates for signed measures if bounds for their logarithmic potentials or energy integrals are known a priori. Classical results of Jentzsch and Szegö for the zero distribution of partial sums of power series can be recovered and sharpened by new discrepany estimates, as well as distribution results of Erdös and Turn for zeros of polynomials bounded on compact sets in the complex plane.
Vladimir V. Andrievskii is Assistant Professor of Mathematics at Kent State University. Hans-Peter Blatt is Full Professor of Mathematics at Katholische Universität Eichstätt.

Klappentext

A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.

Inhalt

• Preface Auxiliary Facts Zero Distribution of Polynomials Discrepancy Theorems via Two-Sided Bounds for Potentials Discrepancy Thoerems via One-Sided Bounds for Potentials Discrepancy Theorems via Energy Integrals Applications of Jentzsch-Szegö and Erdös-Turán Type Theorems Applications of Discrepancy Theorems Special Topics Appendix A: Conformally INvariant Characteristics of Curve Families Appendix B: Basics in the Theory of Quasiconformal Mappings Appendix C: Constructive Theory of Functions of a Complex Variable Appendix D: Miscellaneous Topics Bibliography Glossary of Notation Index